A stochastic model demonstrates low-cost meteorological support to environment dependent simulation studies. Only the univariate problem is demonstrated, but extentions to multivariate applications are feasible. This application models atmospheric visibility. The model simulates time series at a given geographical point. A historically derived cumulative frequency distribution is converted to its equivalent normal deviate and fitted by a rational approximation. A Markovian time dependence is assumed. Seasonal and diurnal cycles are modeled. Subsequent values are generated using a time-correlation weighted linear combination of the prior value and a unit normal random input. This produces a Brownian Movement phenomena within the appropriate probability density function. A given run tends to regress toward the climatological mean while exhibiting random fluctuations. A run of sufficient length recreates the probability density functions. Results presented verify model performance against historical data and include a few applications.